I need to write an equation for this graph

Question

I think the equation I'm supposed to use is: f(x)=A*cos(Bx-C)+D

So far I found the amplitude and period which is 2 and pi/2

I'm kinda stuck on how to put it all together and write this equation

(The graph might be too small to see the x values, it didn't let me put a bigger image.

The x-axis is labeled: π/4------π/2-----3π/4-----π-----5π/4-------3π/4--------7π/4)

Answer 1

With the form you gave A would be the amplitude (one half the distance from the max to the min), B would be 2π/T where T is the period (how long on the x-axis it takes to repeat), D would be the vertical translation (how far it's moved up), and C would be the phase shift which we can find given one point on the graph. You measured the amplitude and period, and it looks like it's shifted up 4. That would give us

f(x)=2cos(4x-C)+4.

Using the point f(0) = 4, 4 = 2 cos(2⋅0-C) + 4, and cos(-C) = 0. As the cosine is an even function cos(C) = 0. Then

C = arccos(0) = π/2.

f(x) = 2 cos(4 x - π/2) + 4.

The graph is not clear so try graphing that and see if it matches.